1D Transient Heat Conduction CDF Tool
Analytic Solution for 1D Transient Heat Conduction
The problem geometry and boundary conditions are shown below. An initially isothermal (Tinitial) semi-infinite medium is suddenly subject to a surface temperature Th.
The temperature field can be non-dimensionalized as:
The governing differential equation (with spatially one-dimensional heat flow) is
The solution for all locations x and times t is:
![\theta(x,t) = 1-\text{erf}\left[\frac{x}{2\sqrt{\alpha t}}\right]](/site/wiki/math/8/f/e/8fe83094a7b28f5b0d2ceb365c257fce.png)
where α is the material’s thermal diffusivity.
Graphical CDF Tool
The following is an embedded, active Mathematica CDF tool. The units for α are cm2/sec, with corresponding units of cm and sec for x and t, respectively.